The results of the previous Section clearly show the relevance of future GW detectors to test our scenario across a very wide range of frequencies. In particular, we have demonstrated how several physical mechanisms leave distinct imprints on the SGWB by distorting its spectral shape in different ways. Therefore, an interesting question that arises quite naturally is whether we can hope or not to reconstruct such peculiar spectral shapes using future observations of the SGWB. Before answering such a question, it is important to mention that sophisticated techniques to reconstruct the frequency dependence of the SGWB have been recently developed within the LISA collaboration [1]}, [2]} and in other works [3]}, [4]}, [5]}. While such techniques are the state of the art of the reconstruction of the SGWB, we adopt in this paper the much simpler (and as such more qualitative) approach of the Power Law Sensitivity curve (PLS) introduced in Ref. [6]} and further generalized to the case of SGWB with a non-trivial spectral shape. This technique is helpful to show qualitatively at which level GW detectors can reconstruct the signal.
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